Definition:Rank (Linear Algebra)

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Definition

Linear Transformation

Let $\phi$ be a linear transformation from one vector space to another.

Let the image of $\phi$ be finite-dimensional.


Then its dimension is called the rank of $\phi$ and is denoted $\map \rho \phi$.


Matrix

The rank of $\mathbf A$, denoted $\map \rho {\mathbf A}$, is the dimension of the subspace of $K^m$ generated by the columns of $\mathbf A$.


That is, it is the dimension of the column space of $\mathbf A$.




Also see